• The Min Max algorithm is a decision-making algorithm used in the field of game theory and artificial intelligence.
• It is used to determine the optimal move for a player in a two-player game by considering all possible outcomes of the game.
• The algorithm helps in selecting the move that minimizes the maximum possible loss. The Min Max algorithm has many applications in game AI, decision-making, and optimization

Mini-Max Algorithm in Artificial Intelligence

• Mini-max algorithm is a recursive or backtracking algorithm which is used in decision-making and game theory. It provides an optimal move for the player assuming that opponent is also playing optimally.
• Mini-Max algorithm uses recursion to search through the game-tree.
• Min-Max algorithm is mostly used for game playing in AI. Such as Chess, Checkers, tic-tac-toe, go, and various tow-players game. This Algorithm computes the minimax decision for the current state.
• In this algorithm two players play the game, one is called MAX and other is called MIN.
• Both the players fight it as the opponent player gets the minimum benefit while they get the maximum benefit.
• Both Players of the game are opponent of each other, where MAX will select the maximized value and MIN will select the minimized value.
• The minimax algorithm performs a depth-first search algorithm for the exploration of the complete game tree.
• The minimax algorithm proceeds all the way down to the terminal node of the tree, then backtrack the tree as the recursion.

Working of Min-Max Algorithm:

• The working of the minimax algorithm can be easily described using an example. Below we have taken an example of game-tree which is representing the two-player game.
• In this example, there are two players one is called Maximizer and other is called Minimizer.
• Maximizer will try to get the Maximum possible score, and Minimizer will try to get the minimum possible score.
• This algorithm applies DFS, so in this game-tree, we have to go all the way through the leaves to reach the terminal nodes.

Step-1: In the first step, the algorithm generates the entire game-tree and apply the utility function to get the utility values for the terminal states. In the below tree diagram, let's take A is the initial state of the tree. Suppose maximizer takes first turn which has worst-case initial value =- infinity, and minimizer will take next turn which has worst-case initial value = +infinity.

Step 2: Next, we determine the utility values for the Maximizer. Starting with an initial value of -∞, we compare each terminal state value with the Maximizer's current value and select the higher one. This process finds the maximum value among all options.

• For node D: max(-1, 4) = 4